      program Ex4b_GaussLegendre

      implicit none
      dimension Ai(6),y(6)
      real*8 f,Ai,y,z,sum,integral,log
      real*8,parameter::Pi=3.141592654
      integer k,j,i

      data(Ai(i),i=1,6)/0.171324492,0.360761573,0.467913935,0.467913935,0.360761573,0.171324492/
      data(y(j),j=1,6)/-0.932469514,-0.661209386,-0.238619186,0.238619186,0.661209386,0.932469514/
      sum=0.0
      do k=1,6
        z=y(k)
      	sum=sum+Ai(k)*f(z)
      enddo
      integral=sum

      print*,'Number of points = ',6
      print*,'Integral = ',integral

      end

      real*8 function f(z)
      real*8,parameter::Pi=3.141592654
      real*8 z
      f=(Pi/4.)*log(((Pi/4.)*(1+z))+1)
      return
      end